Affinity Propagation and Uncapacitated Facility Location Problems

One of the most important distinctions that must be made in clustering research is the difference between models (or problems) and the methods for solving those problems. Nowhere is this more evident than with the evaluation of the popular affinity propagation algorithm (apcluster.m), which is a MATLAB implementation of a neural clustering method that has received significant attention in the biological sciences and other disciplines. Several authors have undertaken comparisons of apcluster.m with methods designed for models that fall within the class of uncapacitated facility location problems (UFLPs). These comparative models include the p-center (or K-center) model and, more importantly, the p-median (or K-median) model. The results across studies are conflicting and clouded by the fact that, although similar, the optimization model underlying apcluster.m is slightly different from the p-median model and appreciably different from the pcenter model. In this paper, we clarify that apcluster.m is actually a heuristic for a 'maximization version' of another model in the class of UFLPs, which is known as the simple plant location problem (SPLP). An exact method for the SPLP is described, and the apcluster.m program is compared to a fast heuristic procedure (sasplp.m) in both a simulation experiment and across numerous datasets from the literature. Although the exact method is the preferred approach when computationally feasible, both apcluster.m and sasplp.m are efficient and effective heuristic approaches, with the latter slightly outperforming the former in most instances.